Kind of confused and really hoping you can explain lollll. By drilling do you mean taking a PT? Like where would we find drills outside of the drills given?

Me too pls!

I know M means most.... but I too would love it if someone could clarify what A B and C mean. I have an idea but would like some clarification if anyone is willing to #help.

Ok so I was a bit confused on this example until I honestly dropped the Lawgic and just used my intuition.....

So the statement reads: "Most classically trained opera singers can recite the lyrics to Musetta's Waltz and most people who have not received such training cannot. It seems likely, therefore, that Anna, who can recite the lyrics to Musetta's Waltz, was classically trained."

Lets break it down though, basically the part that says "most classically trained opera singers can recite the lyrics to Musetta's Waltz" is sayin that of all the classically trained opera singers in the world, most of them can recite the lyrics to Musetta's Waltz. And intuitively this makes sense, because as people who are classically trained, you'd expect that most of them know the lyrics to Musetta's Waltz.... or in other words, you'd expect someone in that field to know about the music within their field.

Now let's look at the next part..." most people who have not received such training cannot."

Ok, so this is saying that if you are not one of those people who is a classically trained opera singer, then you probably cannot recite the lyrics to Musetta's Waltz. And honestly, this makes sense because, for example, I am not someone who is a classically trained opera singer and I cannot recite Musetta's Waltz lyrics to you if you asked lolll. And tbh if you asked my friends who are also not classically trained opera singers, they most definitely would not be able to recite the lyrics either. But that's just me and my friends, not the whole world. It's entirely possible, and very likely, that there are people in the world who, like my friends and I, are not classically trained opera singers but CAN recite the lyrics to Musetta's Waltz.

That being said, if we take the last sentence, "It seems likely, therefore, that Anna, who can recite the lyrics to Musetta's Waltz, was classically trained." it is not valid because the writer is making a HUGE assumption.

They are saying that because Anna can recite the lyrics to Musetta's Waltz she must have been classically trained. But that's just not true. What if Anna is just one of those people in the world who is not a classically trained person but can recite the lyrics? It is entirely possible that Anna can recite Musetta's lyrics simply because she heard it, idk, on the radio or something and now she can recite it.

Thus, the statement at the end is a false implication. I hope I didn't confuse anyone further, but this is how I broke it down in my head, so hopefully this helps someone lol.

Could someone please help me wrap my head around the lawgic behind this sentence... "We will meet our environmental goals only if most cars become electric."?

I am currently reading it as:

Meet Enviro Goals → most cars become electric

Is this right? Also if anyone could please better explain what he means here:

What if all cars became electric? No. Clearly, if all cars became electric, that would be just fine. That would not constitute a failure of the necessary condition because that usage of "most" required us to understand that it could include "all."

#help pleaseeeee

Hi Jack! I too was confused on this one for a while but once I spent hours digesting it this is what I was able to figure out.

So basically the statement says "If a pet adoption center has an interactive website and is a 501(c)3 non-profit then it will be eligible for the Mittens Foundation Grant." So lawgically it can be represented as (IW and 501c → Eligible). In other words, knowing that a pet adoption center has an interactive website AND is a 501(c)3 non-profit is sufficient (good enough) information to conclude that they are eligible for the grant. However, if we flipped this around (say we did [IE and 501(c) ← Eligible] ... that is if we said 'Being eligible for the grant is sufficient (good enough) information to assume that the center has both an Interactive website and is a 501(c) then this would not be correct. That's because saying a center is eligible is not sufficient info to tell us that they have these two things. Perhaps they don't have an interactive website but they are still eligible. We cannot assume this, and we see why when we take the contrapositive.

The contrapositive can be lawgically represented as [/eligible → /IW or /501c]. Or in other words, a pet center that is not eligible for the grant if they either do not have an interactive website or they are not a 501c. Now since we already established that having an interactive website and being a 501c is sufficient (good enough) info to assume that the center is eligible for the grant then it makes sense that if they aren't eligible then at the very least we can say that they don't have either of these two things... because if they did then we would know that they are eligible for the grant.

All we know from the original sentence is that [IW and 501c → Eligible] but nowhere in the sentence does it say that you MUST have these two things, it only says that having these two things is sufficient (good enough) info to make you eligible. In other words, there might be other things that would make one eligible for the grant but here all the information they are telling us is that, at the very least, if you have these two things then it's safe to assume you are eligible for the grant.

Not sure if this helped you out, but this is more or less how I came to understand it!

How does or change to and? I am s confused please #help

Honestly, this made no sense to me before, but once I compared it to another example that we have done before it made more sense.

The example I used was "If one is a cat, then one is a mammal." So from past lessons, we learned that "If one is a cat" is the sufficient condition, and "then one is a mammal" is the necessary condition. In other words, being a cat is sufficient (good enough) information to assume that one is a mammal. (Which can be lawgically represented as C → M). However, if you went the other way (if you lawgically do C ← M [which can be read "if one is a mammal then one is a cat"]) this statement would not be accurate. That's because knowing something is a mammal is not sufficient (good enough) information to assume that they are a cat (and in this case that makes sense right? Like there are plenty of other mammals that are not cats.)

Therefore, using that same lawgic can help with the Kumar example. The example says: Students are cited as "late" only if they arrive more than five minutes past the last ring of the homeroom bell. For this example, "Students are cited as late" is the sufficient (good enough) condition, and "arriving more than five minutes late" is the necessary condition (Which can lawgically be represented as Cited Late → 5+). However, again here if you went the other way (that is, if you lawgically do Cited Late ← 5+ [which can be read "if one is arrives more than 5 minutes after the bell, then one is cited as late]) this statement would not be accurate. That's because knowing that someone arrived 5 minutes after school starts is NOT sufficient (good enough) information to assume that they were cited as late. This also makes sense if you think of it too, there are plenty of reasons that Kumar, who arrived 17 minutes late, did not get cited as late... for example, he could have been excused, or he could have had a chill teacher who just didn't care.

Anyways that's what helped me most because I was really confused about this one until I started comparing it to others that made more sense to me. Another thing I did was change the indicator... Instead of saying "Only if" I used "only when" because Idky but that just made more sense to me.

Hope this helps, and feel free to correct me if I am wrong in any way!

Yes! Thank you sooo much!!

Could anyone explain this to me please: "If X, Y" says that X is sufficient for Y and Y is necessary for X.

I am very confused and would appreciate any #help

I am a bit confused about what makes the first conditional argument specific and the other abstract in the image at the end (is it because one is using examples like luke, jedi, the force while the other is simply using variables?) ... this may be a dumb question #help